Quark–hadron phase transitions in brane-world cosmologies

Abstract

When the universe was about 10 µseconds old, a first order cosmological quark -hadron phase transition occurred at a critical temperature of around 200 MeV. In this work, we study the quarkhadron phase transition in the context of brane-world cosmologies, in which our Universe is a three-brane embedded in a five-dimensional bulk, and within an effective model of QCD. We analyze the evolution of the physical quantities, relevant for the physical description of the early universe, namely, the energy density, temperature and scale factor, before, during, and after the phase transition. To study the cosmological dynamics and evolution we use both analytical and numerical methods. In particular, due to the high energy density in the early Universe, we consider in detail the specific brane world model case of neglecting the terms linearly proportional to the energy density with respect to the quadratic terms. A small brane tension and a high value of the dark radiation term tend to decrease the effective temperature of the quark-gluon plasma and of the hadronic fluid, respectively, and to significantly accelerate the transition to a pure hadronic phase. By assuming that the phase transition may be described by an effective nucleation theory, we also consider the case where the Universe evolved through a mixed phase with a small initial supercooling and monotonically growing hadronic bubbles. PACS numbers: 04.50.-h, 98.80.Cq, 98.80.Bp, 98.80.Jk I. INTRODUCTIONThe possibility that our 4D universe may be viewed as a brane hypersurface embedded in a higher dimensional bulk space has attracted considerable interest lately. A scenario with an infinite fifth dimension in the presence of a brane can generate a theory of gravity which mimics purely four-dimensional gravity, both with respect to the classical gravitational potential and with respect to gravitational radiation [1]. The gravitational self-couplings are not significantly modified in this model. This result has been obtained from the study of a single 3-brane embedded in five dimensions, with the 5D metric given by ds 2 = e −f (y) η µν dx µ dx ν + dy 2 , which can produce a large hierarchy between the scale of particle physics and gravity due to the appearance of the warp factor [1]. Even if the fifth dimension is uncompactified, standard 4D gravity is reproduced on the brane. In contrast to the compactified case, this follows because the near-brane geometry traps the massless graviton. Hence this model allows the presence of large or even infinite non-compact extra dimensions. Our brane is identified to a domain wall in a 5-dimensional anti-de Sitter space-time.The effective gravitational field equations on the brane-world, in which all the matter forces except gravity are confined on the 3-brane in a 5-dimensional space-time with Z 2 -symmetry have been obtained, by using an elegant geometric approach, in [2,3]. The correct signature for gravity is provided by the brane with positive tension. If the bulk space-time is exactly anti-de Sitter, then generically the m...

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